what are the differences between linux and unix?

UNIX is copyrighted name, only big companies are allowed to use the UNIX copyright and name, so IBM AIX and Sun Solaris and HP-UX all are UNIX operating systems. The Open Group holds the UNIX trademark in trust for the industry, and manages the UNIX trademark licensing program. We can also say that Linux is a UNIX Clone
But if you consider Portable Operating System Interface (POSIX) standards then Linux can be considered as UNIX. In other words you can say that Linux is a Unix clone written from scratch by Linus Torvalds with assistance from a loosely-knit team of hackers across the Net. It aims towards POSIX compliance.
Now let us take a look at some of the major differences.
Linux Is Just a Kernel:-Linux is just a kernel. All Linux distributions includes GUI system + GNU utilities (such as cp, mv, ls,date, bash etc) + installation & management tools + GNU c/c++ Compilers + Editors (vi) + and various applications (such as Open Office, Firefox). However, most UNIX operating systems are considered as a complete operating system as everything come from a single source or vendor.
License and costLinux is Free:- You can download it from the Internet or redistribute it under GNU licenses. You will see the best community support for Linux. Most UNIX like operating systems are not free (but this is changing fast, for example OpenSolaris UNIX). However, some Linux distributions such as Redhat / Novell provides additional Linux support, consultancy, bug fixing, and training for additional fees.
User-Friendly:-Linux is considered as most user friendly UNIX like operating systems. It makes it easy to install sound card, flash players, and other desktop goodies. However, Apple OS X is most popular UNIX operating system for desktop usage.
Security Firewall Software:-Linux comes with open source netfilter/iptables based firewall tool to protect your server and desktop from the crackers and hackers. UNIX operating systems comes with its own firewall product (for example Solaris UNIX comes with ipfilter based firewall) or you need to purchase 3rd party software such as Checkpoint UNIX firewall.
Backup and Recovery Software:-UNIX and Linux comes with different set of tools for backing up data to tape and other backup media. However, both of them share some common tools such as tar, dump/restore, and cpio etc.
File Systems:-Linux by default supports and use ext3 or ext4 file systems.But UNIX comes with various file systems such as jfs, gpfs (AIX), jfs, gpfs (HP-UX), jfs, gpfs (Solaris).